Semiconductor lasers are components frequently used in modern optical communication systems. Semiconductor lasers can be directly operated and modulated by external current sources. By employing well-established nanofabrication techniques including photo- (electron beam-) lithography, dry etching, and wet-chemical etching processes, a dense array of some of the high performance semiconductor lasers including vertical cavity surface emitting lasers (VCSELs) can be fabricated on a single chip. In particular, for long distance fiber optic communications, semiconductor lasers that emit 1.3 μm or 1.5 μm in the wavelength are more attractive.
It has been well established that cavities having both sufficiently low optical loss and submicron-sized mode volume can be used to greatly enhance the spontaneous emission coupling factor (β), which is defined as a fraction of a number of photons couples into a specific optical mode of interest (laser mode) over a total number of all the spontaneously emitted photons. The threshold of a laser, which is one important figure of merit for a given semiconductor laser, is closely related to β. It is intuitively clear that, the so called threshold-less laser may be achieved by utilizing a laser cavity with β=1. VCSELs are known to have relatively small mode volume compared with other semiconductor lasers, a typical β for VCSELs on the order of ˜10−4. Furthermore, it has been recently shown that utilizing a large β>0.1 cavity may enable a new pathway to achieve ultra-high modulation speed far greater than 100 Gb/s (see, for example, reference 10). Conventional semiconductor lasers can be modulated within an approximate range of 20 to 40 Gb/s.
A photonic crystal which consists of a periodic arrangement of (low and high) dielectric materials has been proved to be very useful to achieve submicron-sized optical cavities with a large β>0.1 (see, for example, references 3, 9, and 14). The most widely adopted geometry in the field of photonic crystal lasers is a photonic crystal slab structure that is made of an optically thin dielectric slab with a periodic arrangement of perforated air-holes. Spatially localized electric-field intensity distributions (optical resonant modes) may be formed at around a crystal ‘defect region’, which has slightly higher effective refractive index than its outside region. To achieve laser operation, a certain type of gain materials such as multiple quantum wells can be inserted in the middle of the slab during the epitaxial growth process.
The first semiconductor photonic crystal slab defect laser was operated by optical pumping at liquid nitrogen temperature (see, for example, reference 2). However, thereafter, much progress has been made to achieve optimized cavity quality factors (Q) along with the rapid development of numerical simulation techniques for electrodynamics such as the finite-difference time-domain (FDTD) method. Nowadays the state of the art photonic crystal cavity design enables a Q factor exceeding over 1 million (see, for example, reference 18) and very recently, room-temperature continuous-wave operation by optical pumping was reported from a certain type of defect design (see, for example, reference 7, 8, and 14).
Until recently, it has been believed that the semiconductor photonic crystal slab that has, normally, a high refractive index (n>3) should be suspended in air to support reasonably high Q factors. A certain form of electrically-pumped photonic crystal lasers were proposed and demonstrated, in which a submicron-sized dielectric post is formed as a current path (see, for example, reference 9). The record threshold current from such electrically-pumped lasers is approximately 100 μA (see, for example, reference 19). Such device has a resistance of more than 2 kΩ and a thermal characteristic such that a resulting maximum continuous operation time of the device is typically within 10 ns. Moreover, cooling down such device (e.g., for about 1 μs) for the next operation involves shutting off the device.
FIG. 1A shows a top view of a known photonic crystal design. Circular background air-holes (15) arranged in a triangular lattice (11) in a semiconductor slab serve as photonic band-gap material, by which light propagation in the horizontal directions within a certain frequency range is prohibitive (see, for example, reference 1). As shown in FIG. 1B, by forming a defect region (14) in a perfectly periodic photonic crystal, strong light localization is enabled. The exemplary defect region (14) of FIG. 1B is formed by pushing away six nearest air-holes from a center of the defect region (14) and reducing radii of the six air-holes to generate modified air-holes (12, 13) (see, for example, reference 3). Structural parameters related to the photonic crystal of FIG. 1B are shown in FIG. 1C. Radii of air-holes (12, 13) are denoted respectively by ‘rm’ and ‘rm+Δ’. A lattice constant ‘a’ is also shown in FIG. 1C and each of the background air-holes (15) has a radius denoted by ‘r’. Typically the radii ‘r’ and ‘rm’ are chosen to be approximately equal to 0.35a and 0.25a respectively.
Referring to FIGS. 1A-C, several resonant modes having different eigen-frequencies can coexist in the same defect geometry. They are denoted by the dipole (doubly degenerate), the quadrupole (doubly degenerate), the hexapole (non-degenerate), and the monopole (non-degenerate) modes, depending on their rotational symmetries (see, for example, reference 3). Full vectorial 3-D numerical simulations, such as FDTD can be used to understand properties of the photonic crystal cavity modes (see, for example, reference 4, 13). One may break the perfect six-fold symmetry by slightly increasing the two air-holes facing each other in an x direction, shown with an arrow (17) in FIG. 1A (see, for example, reference 5). This type of perturbation may be employed to break the inherent degeneracy of modes and/or to control the direction of linear polarizations.
One of the important figure of merits in the description of a photonic crystal cavity is a cavity quality factor Q. Thus, a better optical confinement means a higher Q factor. In all 2-D photonic crystal slab structures, major optical losses occur in the vertical directions, through the top and bottom of the slab. This incomplete vertical confinement may be understood by the notion of the total-internal-reflection (see, for example, reference 6). Therefore, the best vertical confinement may be obtained by maximizing the refractive index contrast between the slab material and surrounding media (claddings). For telecom wavelength (1.3 μm or 1.55 μm) applications, InGaAsP (Indium Gallium Arsenic Phosphate) material system may be employed as a slab material and it has a high refractive index of approximately 3.45. Therefore, the use of air as a cladding material seems to be natural starting point when one wants to optimize Q factors.
To improve thermal characteristics of 2-D photonic crystal slab devices, the use of silica or sapphire as a bottom cladding material has been proposed and demonstrated (see, for example, references 7-8). The Q factor obtained using such material is around 2000. The mentioned materials are electrical insulators.
A light extraction efficiency of 50% can be achieved using conventional photonic crystal slab nanolasers (see, for example, references 2, 3, 9, 10, and 12) due to the vertically symmetric slab geometries. Some of the plasmonic cavity designs have been drawn much attention, recently (see, for example, references 15 and 16). Due to metal loss, radiation efficiencies below 10% can be achieved with such designs.